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Automatic estimation of multivariate spectra via smoothing splines

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  • Ori Rosen
  • David S. Stoffer
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    Abstract

    The classical method for estimating the spectral density of a multivariate time series is first to calculate the periodogram, and then to smooth it to obtain a consistent estimator. Typically, to ensure the estimate is positive definite, all the elements of the periodogram are smoothed the same way. There are, however, many situations for which different components of the spectral matrix have different degrees of smoothness. We propose a Bayesian approach that uses Markov chain Monte Carlo techniques to fit smoothing splines to each component, real and imaginary, of the Cholesky decomposition of the periodogram matrix. The spectral estimator is then obtained by reconstructing the spectral estimator from the smoothed Cholesky decomposition components. Our technique produces an automatically smoothed spectral matrix estimator along with samples from the posterior distributions of the parameters to facilitate inference. Copyright 2007, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 94 (2007)
    Issue (Month): 2 ()
    Pages: 335-345

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    Handle: RePEc:oup:biomet:v:94:y:2007:i:2:p:335-345

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    Cited by:
    1. Jan Beran & Mark A. Heiler, 2007. "Estimation of a nonparametric regression spectrum for multivariate time series," CoFE Discussion Paper 07-12, Center of Finance and Econometrics, University of Konstanz.
    2. Rosen, Ori & Thompson, Wesley K., 2009. "A Bayesian regression model for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3773-3786, September.
    3. Christian Macaro & Raquel Prado, 2014. "Spectral Decompositions of Multiple Time Series: A Bayesian Non-parametric Approach," Psychometrika, Springer, vol. 79(1), pages 105-129, January.

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